Average of a Stream of Numbers

Last Updated : 10 May, 2026

Given an array arr[], find the average or mean of the prefix array at every index.

Examples:

Input: arr[] = [10, 20, 30, 40, 50]
Output: [10, 15, 20, 25, 30]
Explanation: 10 / 1 = 10, (10 + 20) / 2 = 15, (10 + 20 + 30) / 3 = 20 and so on.

Input: arr[] = [12, 1]
Output: [12, 6]
Explanation: 12 / 1 = 12, (12 + 1) / 2 = 6

Try It Yourself

Table of Content

Computing Running Sum - O(n) Time
Running Average to Avoid Overflow - O(n) Time

Computing Running Sum - O(n) Time

The idea is to compute sum till every point and compute average at every point. The problem with this solution is, it causes overflow even for small values.

Let us understand with an example:

Input: arr[] = 10, 20, 30, 40, 50
Start traversal: Initialize avg = 0

At 10 -> sum = 10, store 10 / 1 = 10
At 20 -> sum = 30, store 30 / 2 = 15
At 30 -> sum = 60, store 60 / 3 = 20
At 40 -> sum = 100, store 100 / 4 = 25
At 50 -> sum = 150, store 150 / 5 = 30

All elements processed. Final array = 10, 15, 20, 25, 30

C++

#include <iostream>
using namespace std;

// Prints sum of a stream of numbers
vector<int> prefixSum(vector<int> &arr)
{
    int n = arr.size();

    // initialize a vector to store the sum values
    vector<int> ans(n, 0);

    // initialize a variable to store the sum of numbers
    int sum = 0;

    // iterate through the array
    for (int i = 0; i < n; i++)
    {
        // add the current number to the sum
        sum += arr[i];

        // store the sum in the vector
        ans[i] = sum/(i+1);
    }

    // return the vector of sum values
    return ans;
}

// Driver Code
int main() {
    vector<int> arr = {10, 20, 30, 40, 50};

    vector<int> res = prefixSum(arr);

    for (int i = 0; i < res.size(); i++) {
        cout << res[i] << " ";
    }

    return 0;
}

Java

import java.util.ArrayList;
import java.util.Arrays;

// Prints sum of a stream of numbers
public class Main {
    public static ArrayList<Integer> prefixSum(int[] arr) {
        int n = arr.length;

        // initialize an ArrayList to store the sum values
        ArrayList<Integer> ans = new ArrayList<>(Arrays.asList(new Integer[n]));

        // initialize a variable to store the sum of numbers
        int sum = 0;

        // iterate through the array
        for (int i = 0; i < n; i++) {
            
            // add the current number to the sum
            sum += arr[i];

            // store the sum in the ArrayList
            ans.set(i, sum / (i + 1));
        }

        // return the ArrayList of sum values
        return ans;
    }

    // Driver Code
    public static void main(String[] args) {
        int[] arr = {10, 20, 30, 40, 50};

        ArrayList<Integer> res = prefixSum(arr);

        for (int i = 0; i < res.size(); i++) {
            System.out.print(res.get(i) + " ");
        }
    }
}

Python

def prefixSum(arr):
    n = len(arr)

    # initialize a list to store the sum values
    ans = [0] * n

    # initialize a variable to store the sum of numbers
    sum = 0

    # iterate through the array
    for i in range(n):
        
        # add the current number to the sum
        sum += arr[i]

        # store the sum in the list
        ans[i] = sum // (i + 1)

    # return the list of sum values
    return ans

# Driver Code
arr = [10, 20, 30, 40, 50]
res = prefixSum(arr)
for i in range(len(res)):
    print(res[i], end=' ')

C#

using System;
using System.Collections.Generic;

// Prints sum of a stream of numbers
public class Program
{
    public static List<int> prefixSum(int[] arr)
    {
        int n = arr.Length;

        // initialize a list to store the sum values
        List<int> ans = new List<int>(new int[n]);

        // initialize a variable to store the sum of numbers
        int sum = 0;

        // iterate through the array
        for (int i = 0; i < n; i++)
        {
            // add the current number to the sum
            sum += arr[i];

            // store the sum in the list
            ans[i] = sum / (i + 1);
        }

        // return the list of sum values
        return ans;
    }

    // Driver Code
    public static void Main()
    {
        int[] arr = { 10, 20, 30, 40, 50 };

        List<int> res = prefixSum(arr);

        for (int i = 0; i < res.Count; i++)
        {
            Console.Write(res[i] + " ");
        }
    }
}

JavaScript

// Prints sum of a stream of numbers
function prefixSum(arr) {
    let n = arr.length;

    // initialize an array to store the sum values
    let ans = new Array(n).fill(0);

    // initialize a variable to store the sum of numbers
    let sum = 0;

    // iterate through the array
    for (let i = 0; i < n; i++) {
        // add the current number to the sum
        sum += arr[i];

        // store the sum in the array
        ans[i] = Math.floor(sum / (i + 1));
    }

    // return the array of sum values
    return ans;
}

// Driver Code
let arr = [10, 20, 30, 40, 50];
let res = prefixSum(arr);
for (let i = 0; i < res.length; i++) {
    console.log(res[i] + ' ');
}

Output

10 15 20 25 30

Running Average to Avoid Overflow - O(n) Time

The idea is to avoid overflow by avoiding sum computation.

The idea is to maintain a variable avg to store the running sum and traverse the array from left to right. At each index i, we add the current element to avg, then compute the average as avg / (i + 1) and store it in the result array.

Let us understand with an example:

Input: arr[] = [1, 3, 4, 2, 6, 5, 8, 7]
Start traversal: Initialize avg = 0

At 1 -> avg = 1
At 3 -> avg = 1 + (3 - 1)/2 = 2
At 4 -> avg = 2 + (4 - 2)/3 = 2.67
At 2 -> avg = 2.67 + (2 - 2.67)/4 = 2.5
At 6 -> avg = 3.2
At 5 -> avg = 3.5
At 8 -> avg ≈ 4.14
At 7 -> avg = 4.5

C++

#include <iostream>
#include <vector>
using namespace std;

vector<int> prefixAvg(vector<int> &arr)
{
    vector<int> res;
    long double avg = 0;
    int n = arr.size();

    for (int i = 0; i < n; i++)
    {
        // Update avg
        avg += (arr[i] - avg) / (i + 1);

        res.push_back((int)avg);
    }
    return res;
}

// Driver Code
int main()
{
    vector<int> arr = {10, 20, 30, 40, 50};

    vector<int> res = prefixAvg(arr);

    for (int i = 0; i < res.size(); i++)
    {
        cout << res[i] << " ";
    }

    return 0;
}

Java

import java.util.ArrayList;
import java.util.List;

public class Main {
    public static List<Integer> prefixAvg(int[] arr) {
        List<Integer> res = new ArrayList<>();
        double avg = 0;
        int n = arr.length;

        for (int i = 0; i < n; i++) {
            // Update avg
            avg += (arr[i] - avg) / (i + 1);

            res.add((int)avg);
        }
        return res;
    }

    public static void main(String[] args) {
        int[] arr = {10, 20, 30, 40, 50};

        List<Integer> res = prefixAvg(arr);

        for (int i = 0; i < res.size(); i++) {
            System.out.print(res.get(i) + " ");
        }
    }
}

Python

def prefixAvg(arr):
    res = []
    avg = 0
    n = len(arr)

    for i in range(n):
        # Update avg
        avg += (arr[i] - avg) / (i + 1)

        res.append(int(avg))
    return res

# Driver Code
arr = [10, 20, 30, 40, 50]

res = prefixAvg(arr)

for i in range(len(res)):
    print(res[i], end=' ')

C#

using System;
using System.Collections.Generic;

class Program
{
    static List<int> prefixAvg(List<int> arr)
    {
        List<int> res = new List<int>();
        double avg = 0;
        int n = arr.Count;

        for (int i = 0; i < n; i++)
        {
            // Update avg
            avg += (arr[i] - avg) / (i + 1);

            res.Add((int)avg);
        }
        return res;
    }

    // Driver Code
    static void Main()
    {
        List<int> arr = new List<int> {10, 20, 30, 40, 50};

        List<int> res = prefixAvg(arr);

        for (int i = 0; i < res.Count; i++)
        {
            Console.Write(res[i] + " ");
        }
    }
}

JavaScript

function prefixAvg(arr) {
    let res = [];
    let avg = 0;
    let n = arr.length;

    for (let i = 0; i < n; i++) {
        // Update avg
        avg += (arr[i] - avg) / (i + 1);

        res.push(Math.floor(avg));
    }
    return res;
}

// Driver Code
let arr = [10, 20, 30, 40, 50];

let res = prefixAvg(arr);

for (let i = 0; i < res.length; i++) {
    console.log(res[i] + " ");
}

Output

10 15 20 25 30

Time Complexity: O(n)
Auxiliary Space: O(n)

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